Question

Find \(\frac{dy}{dx}\), if x=2t^2 and y=6t^6.

(a) -9t^4

(b) 9t^4

(c) t^4

(d) 9t^3

I had been asked this question in a job interview.

Question is taken from Derivatives of Functions in Parametric Forms in section Continuity and Differentiability of Mathematics – Class 12

Answer 1

The correct option is (b) 9t^4

The explanation is: Given that, x=2t^2 and y=6t^6

\(\frac{dx}{dt}\)=4t

\(\frac{dy}{dt}\)=36t^5

\(\frac{dy}{dx}\)=\(\frac{dy}{dt}.\frac{dt}{dx}=\frac{36t^5}{4t}=9t^4\)